That's some but not all of the mechanism.
Dutch Roll is a combined rolling and yawing motion, so it is driven by the interaction of the rolling and yawing moments on the aircraft, and the responses to them.
Assuming that the controls are fixed (quite a big assumption in fact) and that there is no longitudinal coupling (another biggie) the main derivatives involved are:
Cn-beta - yaw due to sideslip = "directional stability"
Cn-p - yaw due to roll rate
Cn-r - yaw due to yaw rate = "yaw damping"
Cl-beta - roll due to sideslip = "dihedral effect"
Cl-p - roll due to roll rate = "roll damping"
Cl-r - roll due to yaw rate
So, taking your description (the assumption of a disturbance in sideslip is quite valid):
Let us assume we have gust from the right giving us a right side slipe angle.
The directional stability gives a right yaw into the wind
and the dihedral effect gives a roll.
The outer (left) wing will move faster through the air and create more lift
(Cl-r) and drag
(Cn-r).
More importantly, the fin will also contribute to Cn-r. It's more true to say that as a result of the roll rate and yaw rate which is generated by the sideslip, there are further rolling and yawing moments driven by various components of the airframe
- The net result will be a roll to the right and a yaw to the left.
if the aircraft is stable in both axes - it's possible that one or other effect may be marginally stable or unstable and it takes the other effect to bring the aircraft back towards equilibrium
- When the aircraft now yaws left, the right wing will move faster through the air and we will have a roll to the left and yaw to right.
again, as with the previous comment, it's not just the wing acting, and the wing may not in fact be stabilising
- The sequence is repeated.
You have to view the Dutch Roll as a whole-aircraft mode and consider all the effects together. A "real" DR will also see pitch-coupling, which will further complicate matters.
at least you didn't mention stalling!